Question

A sample of paramagnetic salt contains 2.0 × 1024 atomic dipoleseach of dipole moment 1.5 × 10–23 J T–1. The sample is placed undera homogeneous magnetic field of 0.64 T, and cooled to a temperatureof 4.2 K. The degree of magnetic saturation achieved is equal to 15%.What is the total dipole moment of the sample for a magnetic field of0.98 T and a temperature of 2.8 K? (Assume Curie’s law)

Answer 1

Given: The number of atomic dipoles in the salt sample is 2.0× 10 24 , the dipole moment of each dipole is 1.5× 10 −23 J T -1 , the strength of magnetic field is 0.64 T, the temperature of salt is 4.2 K and the degree of magnetic saturation achieved is 15%.

Total dipole moment of the atomic dipole is given as,

M tot =n×M

Where, n is the total number of dipoles and M is the moment of each dipole.

By substituting the given values in the above expression, we get

M tot =2× 10 24 ×1.5× 10 −23 =30  JT −1

Magnetic saturation is achieved at 15%. Hence, effective dipole moment is given as,

M 1 =0.15×30 =4.5  JT −1

According to Curie’s law,

M 2 M 1 = B 2 B 1 × T 1 T 2

Where, M 1 and M 2 are the effective dipole moments and B 1 and B 2 are the applied magnetic fields.

By substituting the given values in the above expression, we get

M 2 4.5 = 0.98 0.64 × 4.2 2.8 M 2 =10.34  JT −1

Thus, the total dipole moment of the sample for a magnetic field of 0.98 T and temperature of 2.8 K is 10.34  JT −1 .